In the past block walls have for the most part been insulated by pouring a granular insulating material into the cavities after the blocks are in place in the wall. This granular material settles down into the block cavities, leaving uninsulated areas in the wall. Also, there are rigid inserts presently available which are placed into the main core cavities of masonry blocks. However, these inserts leave critical uninsulated areas at the small cavities between the ends of adjacent blocks and also at the mortar joints between adjacent courses of blocks. Thus, heat very easily flows around these rigid inserts and is lost thus seriously reducing the insulating effect of the inserts.